Solve the given equation over the interval [0, 2π): csc^2 x + 2 csc x = 0.

Factor out the GCF which is csc x

Set each factor equal to zero.
 or 
Using the reciprocal sine function we can replace csc in the equations.
 or 
The first equation yields 1 = 0 which is not true. However the second equation does offer 2 possible answers.
When solved for sinx you get 
The sine function is negative in the 3rd and 4th quadrants.
You can use the unit circle or the  feature on your calculator  
 alter radian answer which is probably what you want is 

38 dollars is your answer.